This invention relates to the measurement of certain functional properties of acoustical, mechanical, or electrical systems, or elements of such systems, and more particularly, to an apparatus and method for measuring certain functional properties of that class of oscillatory systems which exhibit nonlinearity of frequency response with changes in the amplitude of excitation of the system. As is well known to those versed in the art, analogies can be made in many instances between mechanical, acoustical, and electrical systems or devices. An electrical circuit can be considered to be a vibrating system, and this immediately suggests analogies between electrical circuits and vibrating systems. Frequently, electrical network analogs are employed in the design of mechanical systems, acoustical devices, and combinations thereof. The analogies between mechanical, acoustical, and electrical impedances are useful in the solution of many design problems because it permits the analysis to be conducted by the equations of electrical circuits. This design methodology is explained in detail in the book "Dynamical Analogies" by Harry F. Olson, published in 1958. Further reference to this subject may be had in the "McGraw-Hill Encyclopedia of Science and Technology" (1966 Edition) under the subject heading "Dynamical Analogies. "
It is frequently desirable to obtain the characteristic impedances of various dynamic or oscillatory systems in order to design or improve devices incorporating such systems. Acoustic impedance, as conventionally defined at a given surface, is the complex ratio of effective sound pressure averaged over the surface to the effective flux (volume velocity or particle velocity multiplied by the surface area) through it. The unit is the newton-second/meter.sup.5, or the mks acoustic ohm. In the cgs system the unit is the dyne-second/centimeter.sup.5. Acoustic impedance, being a complex quantity, can have real and imaginary components analogous to those in electrical impedances.
For a system executing simple harmonic motion, mechanical impedance is defined as the ratio of force to particle velocity. If the force is that which dries the system and the velocity is that of the point of application of the force, the ratio is the input or driving-point impedance. If the velocity is that at some other point, the ratio is the transfer impedance corresponding to the two points. As in the case of electrical impedance, to which it is analogous, mechanical impedance is a complex quantity. The real part, the mechanical resistance, is independent of frequency as the dissipative forces are proportional to velocity; the imaginary part, the mechanical reactance, varies with frequency, becoming zero at the resonant and infinite at the anti-resonant frequencies of the system.
The total opposition that an electrical circuit presents to an alternating current comprises impedance. Electrical impedance is frequently defined as the ratio of the root-mean-square (rms) voltage to the rms current. Dynamic or oscillatory systems of the type herein considered may comprise either acoustical, electrical, or mechanical elements (or combinations thereof) all of which may have generally similar impedance analogies. Heretofore, various means and methods have been proposed for making impedance measurements in such systems. A consideration of acoustic impedance measurement techniques will serve to exemplify the background of the present invention. A widely accepted technique of the prior art for the measurement of acoustical impedance (and/or absorption coefficient) involves the use of a standing-wave tube. Standards for such tubes have been set forth by the American Society for Testing Materials and are described in "Standard Method of Test for Impedance and Absorption of Acoustical Materials by the Tube Method," (ASTM Designation: C 384-58, 1958 - ASTM Std., Part 5, 997-1009, 1961).
In general, prior art methods, including the ASTM standard test, make the tacit assumption that the quantities being measured are functions of frequency but are independent of the intensity of the (sinusoidal) test signal. That is to say that it is assumed that the material is linear in its acoustical behaviour. More recently, when such measurement methods are applied to materials known to be nonlinear, the intensity of the test signal sometimes has been stated as a test condition.
It has now been discovered experimentally that the nonlinearity of an acoustical material has a further consequence. Specifically, if the use of a particular sinusoidal test signal results in the observation of an acoustic impedance Z.sub.1 at frequency F.sub.1, then the superposition of additional sound at frequencies other than F.sub.1, such as for example broadband noise, causes the impedance to change to some value Z.sub.2 even though all measurements are made at the original frequency F.sub.1 only. The more nonlinear the material being tested, the more pronounced this effect becomes. Thus, the impedance at each frequency F.sub.1 is a function of both the level and the spectrum shape of the entire noise present in the material's environment and if the level of a pure tone at F.sub.1 is less than the overall level of the rest of the noise spectrum then the measured impedance becomes independent of the level of the sinusoidal signal at the frequency F.sub.1. This discovery requires the modification of the more usual definition of acoustical impedance to include a statement of the acoustical environment to which the material is exposed.
The present invention, as will be described below, provides a means for modifying and adapting the standard test apparatus and method to conveniently measure acoustic impedance in accordance with the revised definition. As suggested above, the invention similarly extends to, and covers, the analogous disciplines of mechanical and electrical vibratory or oscillatory systems wherein mechanical impedance, or, as the case may be, electrical impedance, can be correctly measured notwithstanding the existence of non-linear response characteristics of the element being measured which would otherwise introduce error into the desired measurement.
It is recognized that prior attempts have been made to calculate the impedance of nonlinear system elements in the presence of noise. The problem involves the mathematical intractibility which characterizes nonlinear systems. In principle, however, it is solvable at least by successive approximation. The novel and improved method of the present invention provides a practical means for experimentally checking such analyses.